Abstract
Hybrid nanofluids are a type of nanofluid that is created by combining two different types of nanoparticles with a traditional fluid. These nanofluids have unique physicochemical properties that make them more effective at transferring heat than traditional nanofluids. This research paper focuses on predicting thermal and energy transport in non-Newtonian biomagnetic hybrid nanofluids that contain gold and silver nanoparticles, using Gaussian process regression (GPR). The study uses blood as the traditional fluid and incorporates the effects of thermal radiation, thermophoresis, Brownian motion and activation energy into the model equation. The governing nonlinear partial differential equations are simplified to a set of ordinary differential equations using similarity replacements. The shooting method, along with the Runge–Kutta-Fehlberg fourth–fifth-order scheme, is used to solve the transformed equations using MATLAB. The results of the study are presented through figures and tables, which include the coefficient of skin friction, Nusselt number, Sherwood number and motile microbe’s flux, illustrated with surface plots. The GPR model is developed using four basic function kernels (squared exponential, exponential, rational quadratic and matern32 functions) and evaluated using statistical indicators such as RMSE, MSE, MAE and R. The predicted results and simulated numerical values are in good agreement with the coefficient of determination (R2) of 0.999999 for all parameters. The study also finds that GPR models with exponential kernel functions outperform other kernel functions in both the Oldroyd-B and Casson hybrid nanofluid data sets. However, the findings indicate that nanofluids and hybrid nanofluids have superior thermal qualities and stability, making them promising candidates for various thermal applications including solar thermal systems, automotive cooling systems, heat sinks, engineering, medical areas and thermal energy storage.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- \({\overline{u} }_{{\text{w}}},{\overline{u} }_{{\text{e}}}\) :
-
Stretching and free stream velocity [m/s]
- \({\overline{U} }_{{\text{w}}}, {\overline{U} }_{\infty }\) :
-
Positive constants
- \(m\) :
-
Hartree pressure gradient
- \({B}_{0}\) :
-
Magnetic induction parameter, [T]
- \(\overline{B }\) :
-
Magnetic field
- \({\overline{T} }_{{\text{w}}}, {\overline{T} }_{\infty }\) :
-
Temperature near and far away from the wedge wall, [K]
- \({\overline{C} }_{{\text{w}}},{\overline{C} }_{\infty }\) :
-
Concentration of nanoparticles near and far away from the wedge surface
- \({\overline{N} }_{{\text{w}}},{\overline{N} }_{\infty }\) :
-
Density of motile microbes near and far away from the wedge surface
- \({D}_{{\text{B}}},{D}_{{\text{T}}},{D}_{{\text{n}}}\) :
-
Brownian, thermophoresis and microbes’ diffusion coefficient, [m2/s]
- \(\widetilde{S}\) :
-
Extra stress tensor
- \(P\) :
-
Pressure
- \(I\) :
-
Tensor of the identity
- \(\frac{{\text{d}}}{{\text{d}}\overline{t} }\) :
-
Material time derivative
- \({\widetilde{A}}_{1}\) :
-
First tensor of Rivlin-Erickson
- \(\pi\) :
-
Product component of the distortion rate
- \({p}_{\overline{{\text{y}}} }\) :
-
Yield stress
- \({\mathfrak{e}}_{\mathfrak{i}\mathfrak{j}}\) :
-
Distortion rate of \(\left(\mathfrak{i},\mathfrak{j}\right)\) th element
- \({\pi }_{\mathfrak{c}}\) :
-
Critical value based on Casson non- Newtonian model
- \(b\) :
-
Chemotaxis constant
- \({W}_{{\text{c}}}\) :
-
Extreme speed of cell swimming
- \({E}_{{\text{a}}}\) :
-
Modified Arrhenius function
- \({k}_{{\text{r}}}\) :
-
Rate of chemical reaction, [1/s]
- \({k}_{0}\) :
-
Physical constant
- \({\overline{q} }_{{\text{r}}}\) :
-
Radiative heat transport
- \(\overline{T }\) :
-
Temperature, [K]
- \(\overline{C }\) :
-
Nanoparticle concentration, [moles/kg]
- \(\overline{N }\) :
-
Density of motile microorganisms
- \(\overline{u }, \overline{v }\) :
-
The ingredients of velocity in \(\overline{x }\) and \(\overline{y }\) directions [m/s]
- \(\overline{x }\) :
-
Parallel to the surface of the stretching wedge, [m]
- \(\overline{y }\) :
-
Distance normal to the surface, [m]
- \(f\) :
-
Dimensionless stream function
- \(M\) :
-
Magnetic parameter
- \({\text{Pr}}\) :
-
Prandtl number
- \({R}_{{\text{d}}}\) :
-
Radiation parameter
- \(\sigma\) :
-
Chemical reaction parameter
- \({\text{Nb}}\) :
-
Brownian motion parameter
- \({\text{Nt}}\) :
-
Thermophoresis parameter
- \({\text{Ec}}\) :
-
Eckert number
- \({\text{Le}}\) :
-
Lewis number
- \(E\) :
-
Activation energy parameter
- \({\text{Lb}}\) :
-
Lewis number of bioconvection
- \({\text{Pe}}\) :
-
Peclet number of bioconvection
- \(\overline{{\text{N}}}{{\text{u}} }_{x}\) :
-
Nusselt number
- \(\overline{{\text{S}}}{{\text{h}} }_{x}\) :
-
Sherwood number
- \(\overline{{\text{M}}}{{\text{h}} }_{x}\) :
-
Density of motile microbe’s flux
- \({{\text{Re}}}_{x}\) :
-
Local Reynolds number
- \(\mathcalligra{n}\) :
-
Observations
- \(\mathcal{C}\left(s,{s}{\prime}\right)\) :
-
Covariance or kernel function
- \(l\) :
-
Parameter of length scale
- \(\mathfrak{c}\) :
-
Intercept constant
- \(\chi\) :
-
Similarity variable
- \(\widetilde{\zeta }\) :
-
Cauchy stress tensor
- \({\widetilde{\mu }}_{{\text{B}}}\) :
-
Plastic dynamic viscosity
- \(\tau\) :
-
Ratio of heat capacity
- \({\overline{\Omega } }^{*}\) :
-
Total wedge angle
- \(\widetilde{\mu }\) :
-
Coefficient of viscosity
- \({\widetilde{\Lambda }}_{1}\) :
-
Relaxation time
- \({\widetilde{\Lambda }}_{2}\) :
-
Retardation time
- \({\left(\rho {c}_{{\text{p}}}\right)}_{{\text{np}}},{\left(\rho {c}_{{\text{p}}}\right)}_{{\text{bf}}}\) :
-
The heat capacity of the nanoparticle and the base fluid
- \(\varpi \left(\overline{x },\overline{y }\right)\) :
-
Stream function
- \({\sigma }^{*}\) :
-
The constant of Stefan-Boltzmann, [W/m2 K4]
- \({k}^{*}\) :
-
Coefficient of mean absorption, [1/m]
- \({\varphi }_{{\text{Ag}}},{\varphi }_{{\text{Au}}}\) :
-
Nanoparticle volume fractions of silver and gold
- \({\vartheta }_{{\text{hnf}}}\) :
-
Kinematic viscosity of the hybrid nanofluid, [m2/s]
- \({\rho }_{{\text{hnf}}}\) :
-
Density of the hybrid nanofluid, [kg/m3]
- \({\left({\rho c}_{{\text{p}}}\right)}_{{\text{hnf}}}\) :
-
Heat capacity of the hybrid nanofluid, [kg/m3K]
- \({k}_{{\text{hnf}}}\) :
-
Thermal conductivity of the hybrid nanofluid, [W/m K]
- \({\mu }_{{\text{hnf}}}\) :
-
Dynamic viscosity of the hybrid nanofluid, [kg/m s]
- \({k}_{{\text{nf}}}\) :
-
Thermal conductivity of the nanofluid, [W/m K]
- \({\sigma }_{{\text{bf}}}\) :
-
Electrical conductivity of the base fluid, [S/m]
- \({\mu }_{{\text{bf}}}\) :
-
Dynamic viscosity of the base fluid, [kg/m s]
- \({\vartheta }_{{\text{bf}}}\) :
-
Kinematic viscosity of the base fluid, [m2/s]
- \({\rho }_{{\text{bf}}}\) :
-
Density of the base fluid, [kg/m3]
- \({\left({\rho c}_{{\text{p}}}\right)}_{{\text{bf}}}\) :
-
Heat capacity of the base fluid, [kg/m3K]
- \({k}_{{\text{bf}}}\) :
-
Thermal conductivity of the base nanofluid, [W/m K]
- \({c}_{{\text{p}}}\) :
-
Specific heat
- \(\theta\) :
-
Dimensionless temperature
- \(\phi\) :
-
Dimensionless nanoparticle concentration
- \(\Psi\) :
-
Dimensionless density of motile microbes
- \(\gamma\) :
-
Moving wedge parameter
- \(\beta\) :
-
Parameter of Casson nanofluid
- \({\beta }_{1}\) :
-
Deborah number for relaxation time
- \({\beta }_{2}\) :
-
Deborah number for retardation time
- \(\delta\) :
-
Heat source parameter
- \({\sigma }_{1}\) :
-
Concentration difference parameter
- \(\check{\sigma }\) :
-
Standard deviation of the signal
- \(\varsigma\) :
-
Gamma function
- \({\mathcal{C}}_{\varsigma }\) :
-
Bessel function
- \(\varsigma\) :
-
Smooth factor
- \(\epsilon\) :
-
Gaussian distribution noise value
- \(w\) :
-
Quantities at wall
- \(\infty\) :
-
Quantities at free stream
- \({\text{bf}}\) :
-
Base fluid
- \({\text{nf}}\) :
-
Nanofluid
- \({\text{hnf}}\) :
-
Hybrid nanofluid
- \({\text{Au}},\mathrm{ Ag}\) :
-
Silver and Gold
References
Oldroyd, J.G.: On the formulation of rheological equations of state, Proceedings of the Royal Society of London Series A. Math. Phys. Sci. 200(1063), 523–541 (1950)
Hayat, T.; Muhammad, T.; Shehzad, S.A.; Alsaedi, A.: An analytical solution for magnetohydrodynamic Oldroyd-B nanofluid flow induced by a stretching sheet with heat generation/absorption. Int. J. Therm. Sci. 111, 274–288 (2017)
Reddy, M.G.; Rani, M.S.; Kumar, K.G.; Prasannakumara, B.C.: Cattaneo-Christov heat flux and non-uniform heat-source/sink impacts on radiative Oldroyd-B two-phase flow across a cone/wedge. J. Braz. Soc. Mech. Sci. Eng. 40(2), 1–21 (2018)
Kalyani, K.; Rao, N.S.; Makinde, O.D.; Reddy, M.G.; Rani, M.S.: Influence of viscous dissipation and double stratification on MHD Oldroyd-B fluid over a stretching sheet with uniform heat source. SN Appl. Sci. 1(4), 1–11 (2019)
Tong, Z.W.; Ahmed, B.; Al-Khaled, K.; Khan, S.U.; Khan, M.I.; Ahmad, S.; Malik, M.Y.; Xia, W.F.: Peristaltic blood transport in non-newtonian fluid confined by porous soaked tube: a numerical study through galerkin finite element technique. Arab. J. Sci. Eng. 47, 1019–1031 (2022)
Nayak, M.K.; Saranya, S.; Ganga, B.; Hakeem, A.K.A.; Sharma, R.P.; Makinde, O.D.: Influence of relaxation-retardation viscous dissipation on chemically reactive flow of Oldroyd-B nanofluid with hyperbolic boundary conditions. Heat Transfer 49(8), 4945–4967 (2020)
Ali, B.; Hussain, S.; Nie, Y.; Hussein, A.K.; Habib, D.: Finite element investigation of Dufour and Soret impacts on MHD rotating flow of Oldroyd-B nanofluid over a stretching sheet with double diffusion Cattaneo Christov heat flux model. Powder Technol. 377, 439–452 (2021)
Munir, S.; Maqsood, A.; Farooq, U.; Hussain, M.; Siddiqui, M.I.; Muhammad, T.: Numerical analysis of entropy generation in the stagnation point flow of Oldroyd-B nanofluid. Waves Random Complex Media (2022). https://doi.org/10.1080/17455030.2021.2023782
N. Casson, A flow equation for pigment-oil suspensions of the printing ink type. Rheology of disperse systems (1959).
Raju, C.S.K.; Sandeep, N.: Nonlinear radiative magnetohydrodynamic Falkner-Skan flow of Casson fluid over a wedge. Alex. Eng. J. 55(3), 2045–2054 (2016)
Tamoor, M.; Waqas, M.; Khan, M.I.; Alsaedi, A.; Hayat, T.: Magnetohydrodynamic flow of Casson fluid over a stretching cylinder. Results Phys. 7, 498–502 (2017)
Ullah, I.; Shafie, S.; Khan, I.; Hsiao, K.L.: Brownian diffusion and thermophoresis mechanisms in Casson fluid over a moving wedge. Results Phys. 9, 183–194 (2018)
Rashidi, M.M.; Bagheri, S.; Momoniat, E.; Freidoonimehr, N.: Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. Ain Shams Eng. J. 8(1), 77–85 (2017)
Oyelakin, I.S.; Mondal, S.; Sibanda, P.: Nonlinear radiation in bioconvective Casson nanofluid flow. Int. J. Appl. Comput. Math. 5(5), 1–20 (2019)
Khan, S.; Shu, W.; Ali, M.; Sultan, F.; Shahzad, M.: Numerical simulation for MHD flow of Casson nanofluid by heated surface. Appl. Nanosci. 10(12), 5391–5399 (2020)
Krishna, S.G.; Shanmugapriya, M.: Inquiry of MHD bioconvective non-Newtonian nanofluid flow over a moving wedge using HPM. Materials Today: Proceedings 38, 3297–3305 (2021)
Tawade, J.V.; Guled, C.N.; Noeiaghdam, S.; Fernandez-Gamiz, U.; Govindan, V.; Balamuralitharan, S.: Effects of thermophoresis and Brownian motion for thermal and chemically reacting Casson nanofluid flow over a linearly stretching sheet. Results Eng. 15, 100448 (2022)
S.U.S. Choi (1995), Enhancing thermal conductivity of fluids with nanoparticles Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, FED 231/MD 66: 99–105.
Soomro, F.A.; Khan, Z.H.; Zhang, Q.: Numerical study of entropy generation in MHD water-based carbon nanotubes along an inclined permeable surface. Eur. Phys. J. Plus 132(10), 1–12 (2017)
Turkyilmazoglu, M.: Algebraic solutions of flow and heat for some nanofluids over deformable and permeable surfaces. Int. J. Numer. Meth. Heat Fluid Flow 27(10), 2259–2267 (2017)
Daniel, Y.S.; Aziz, Z.A.; Ismail, Z.; Salah, F.: Impact of thermal radiation on electrical MHD flow of nanofluid over nonlinear stretching sheet with variable thickness. Alex. Eng. J. 57(3), 2187–2197 (2018)
Almutairi, F.; Khaled, S.M.; Ebaid, A.: MHD flow of nanofluid with homogeneous-heterogeneous reactions in a porous medium under the influence of second-order velocity slip. Mathematics 7(3), 220 (2019)
Zhang, X.H.; Abidi, A.; Ahmed, A.E.S.; Khan, M.R.; El-Shorbagy, M.A.; Shutaywi, M.; A. Issakhov A. M. Galal,: MHD stagnation point flow of nanofluid over a curved stretching/shrinking surface subject to the influence of Joule heating and convective condition. Case Stud. Therm. Eng. 26, 101184 (2021)
Hazarika, S.; Ahmed, S.; Chamkha, A.J.: Investigation of nanoparticles Cu, Ag and Fe3O4 on thermophoresis and viscous dissipation of MHD nanofluid over a stretching sheet in a porous regime: a numerical modeling. Math. Comput. Simul 182, 819–837 (2021)
Ali, L.; Ali, B.; Abd Allah, A.M.; Hammouch, Z.; Hussain, S.; Siddique, I.; Huang, Y.: Insight into significance of thermal stratification and radiation on dynamics of micropolar water based TiO2 nanoparticle via finite element simulation. J. Mater. Res. Technol. 19, 4209–4219 (2022)
Lu, D.C.; Farooq, U.; Hayat, T.; Rashidi, M.M.; Ramzan, M.: Computational analysis of three layer fluid model including a nanomaterial layer. Int. J. Heat Mass Transf. 122, 222–228 (2018)
Rahman, M.; Sharif, F.; Turkyilmazoglu, M.; Siddiqui, M.S.: Unsteady three-dimensional magnetohydrodynamics flow of nanofluids over a decelerated rotating disk with uniform suction. Pramana 96(4), 170 (2022)
Turkyilmazoglu, M.: Multiple exact solutions of free convection flows in saturated porous media with variable heat flux. J. Porous Media 25(6), 53–63 (2022)
Turcu, R.; Darabont, A.L.; Nan, A.; Aldea, N.; Macovei, D.; Bica, D.; Biro, L.P.: New polypyrrole-multiwall carbon nanotubes hybrid materials. J. Optoelectron. Adv. Mater. 8(2), 643–647 (2006)
Maskeen, M.M.; Zeeshan, A.; Mehmood, O.U.; Hassan, M.: Heat transfer enhancement in hydromagnetic alumina–copper/water hybrid nanofluid flow over a stretching cylinder. J. Therm. Anal. Calorim. 138(2), 1127–1136 (2019)
Shoaib, M.; Raja, M.A.Z.; Sabir, M.T.; Islam, S.; Shah, Z.; Kumam, P.; Alrabaiah, H.: Numerical investigation for rotating flow of MHD hybrid nanofluid with thermal radiation over a stretching sheet. Sci. Rep. 10(1), 1–15 (2020)
Muhammad, K.; Hayat, T.; Alsaedi, A.: Numerical study for melting heat in dissipative flow of hybrid nanofluid over a variable thicked surface. Int. Commun. Heat Mass Transfer 121, 104805 (2021)
Khan, M.; Alsaduni, I.N.; Alluhaidan, M.; Xia, W.F.; Ibrahim, M.: Evaluating the energy efficiency of a parabolic trough solar collector filled with a hybrid nanofluid by utilizing double fluid system and a novel corrugated absorber tube. J. Taiwan Inst. Chem. Eng. 124, 150–161 (2021)
Khan, U.; Zaib, A.; Waini, I.; Ishak, A.; Sherif, E.S.M.; Xia, W.F.; Muhammad, N.: Impact of Smoluchowski temperature and Maxwell velocity slip conditions on axisymmetric rotated flow of hybrid nanofluid past a porous moving rotating disk. Nanomaterials 12(2), 276 (2022)
Alhussain, Z.A.; Tassaddiq, A.: Thin film blood based casson hybrid nanofluid flow with variable viscosity. Arab. J. Sci. Eng. 47(1), 1087–1094 (2022)
Abbas, N.; Shatanawi, W.; Abodayeh, K.: Computational analysis of MHD nonlinear radiation casson hybrid nanofluid flow at vertical stretching sheet. Symmetry 14(7), 1494 (2022)
Zhang, J.; Raza, A.; Khan, U.; Ali, Q.; Zaib, A.; Weera, W.; Galal, A.M.: Thermophysical study of oldroyd-B Hybrid nanofluid with sinusoidal conditions and permeability: a prabhakar fractional approach. Fract. Fract. 6(7), 357 (2022)
Bestman, A.R.: Natural convection boundary layer with suction and mass transfer in a porous medium. Int. J. Energy Res. 14(4), 389–396 (1990)
Ramzan, M.; Ullah, N.; Chung, J.D.; Lu, D.; Farooq, U.: Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction. Sci. Rep. 7(1), 1–15 (2017)
Irfan, M.; Khan, W.A.; Khan, M.; Gulzar, M.M.: Influence of Arrhenius activation energy in chemically reactive radiative flow of 3D Carreau nanofluid with nonlinear mixed convection. J. Phys. Chem. Solids 125, 141–152 (2019)
Ali, B.; Hussain, S.; Nie, Y.; Rehman, A.U.; Khalid, M.: Buoyancy effetcs on falknerskan flow of a Maxwell nanofluid fluid with activation energy past a wedge: finite element approach. Chin. J. Phys. 68, 368–380 (2020)
Azam, M.; Abbas, Z.: Recent progress in Arrhenius activation energy for radiative heat transport of cross nanofluid over a melting wedge. Propul. Power Res. 10(4), 383–395 (2021)
Shanmugapriya, M.; Sundareswaran, R.; Senthil Kumar, P.: Heat and mass transfer enhancement of MHD hybrid nanofluid flow in the presence of activation energy. Int. J. Chem. Eng. 2021, 1–12 (2021)
Rekha, M.B.; Sarris, I.E.; Madhukesh, J.K.; Raghunatha, K.R.; Prasannakumara, B.C.: Activation energy impact on flow of AA7072-AA7075/Water-Based hybrid nanofluid through a cone, wedge and plate. Micromachines 13(2), 302 (2022)
Plesset, M.S.; Winet, H.: Bioconvection patterns in swimming microorganism cultures as an example of Rayleigh-Taylor instability. Nature 248(5447), 441–443 (1974)
Alsaedi, A.; Khan, M.I.; Farooq, M.; Gull, N.; Hayat, T.: Magnetohydrodynamic (MHD) stratified bioconvective flow of nanofluid due to gyrotactic microorganisms. Adv. Powder Technol. 28(1), 288–298 (2017)
Bhatti, M.M.; Mishra, S.R.; Abbas, T.; Rashidi, M.M.: A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects. Neural Comput. Appl. 30(4), 1237–1249 (2018)
Waqas, H.; Khan, S.U.; Hassan, M.; Bhatti, M.M.; Imran, M.: Analysis on the bioconvection flow of modified second-grade nanofluid containing gyrotactic microorganisms and nanoparticles. J. Mol. Liq. 291, 111231 (2019)
Ahmad, F.; Gul, T.; Khan, I.; Saeed, A.; Selim, M.M.; Kumam, P.; Ali, I.: MHD thin film flow of the Oldroyd-B fluid together with bioconvection and activation energy. Case Stud. Therm. Eng. 27, 101218 (2021)
Wang, F.; Zhang, J.; Algarni, S.; Naveed Khan, M.; Alqahtani, T.; Ahmad, S.: Numerical simulation of hybrid Casson nanofluid flow by the influence of magnetic dipole and gyrotactic microorganism. Waves in Random and Complex Media (2022). https://doi.org/10.1080/17455030.2022.2032866
Grbić, R.; Kurtagić, D.; Slišković, D.: Stream water temperature prediction based on Gaussian process regression. Expert Syst. Appl. 40(18), 7407–7414 (2013)
Jiang, Y.; Jia, J.; Li, Y.; Kou, Y.; Sun, S.: Prediction of gas-liquid two-phase choke flow using Gaussian process regression. Flow Meas. Instrum. 81, 102044 (2021)
Chen, Q.; Li, N.: Thermal response time prediction-based control strategy for radiant floor heating system based on Gaussian process regression. Energy and Buildings 263, 112044 (2022)
Adun, H.; Wole-Osho, I.; Okonkwo, E.C.; Ruwa, T.; Agwa, T.; Onochie, K.; Ukwu, H.; Bamisile, O.; Dagbasi, M.: Estimation of thermophysical property of hybrid nanofluids for solar thermal applications: implementation of novel optimizable Gaussian process regression (O-GPR) approach for viscosity prediction. Neural Comput. Appl. (2022). https://doi.org/10.1007/s00521-022-07038-2
Said, Z.; Sharma, P.; Elavarasan, R.M.; Tiwari, A.K.; Rathod, M.K.: Exploring the specific heat capacity of water-based hybrid nanofluids for solar energy applications: a comparative evaluation of modern ensemble machine learning techniques. J. Energy Stor. 54, 105230 (2022)
Algehyne, E.A.; Aldhabani, M.S.; Saeed, A.; Dawar, A.; Kumam, P.: Mixed convective flow of Casson and Oldroyd-B fluids through a stratified stretching sheet with nonlinear thermal radiation and chemical reaction. J. Taibah Univ. Sci. 16(1), 193–203 (2022)
Ghadikolaei, S.S.; Hosseinzadeh, K.; Ganji, D.D.; Jafari, B.: Nonlinear thermal radiation effect on magneto Casson nanofluid flow with Joule heating effect over an inclined porous stretching sheet. Case Stud. Therm. Eng. 12, 176–187 (2018)
Bilal Ashraf, M.; Hayat, T.; Alsulami, H.: Mixed convection Falkner-Skan wedge flow of an Oldroyd-B fluid in presence of thermal radiation. J. Appl. Fluid Mech. 9(4), 1753–1762 (2016)
Gopi Krishna, S.; Shanmugapriya, M.; Alsinai, A.; Alameri, A.: Prediction of thermal and energy transport of MHD Sutterby hybrid nanofluid flow with activation energy using group method of data Handling (GMDH). Comput. Appl. Math. 41(7), 1–39 (2022)
Gopi Krishna, S.; Shanmugapriya, M.; Senthil Kumar, P.: Prediction of bio-heat and mass transportation in radiative MHD Walter-B nanofluid using MANFIS model. Math. Comput. Simul 201, 49–67 (2022)
Gul, T.; Ali, B.; Alghamdi, W.; Nasir, S.; Saeed, A.; Kumam, P.; Mukhtar, S.; Kumam, W.; Jawad, M.: Mixed convection stagnation point flow of the blood based hybrid nanofluid around a rotating sphere. Sci. Rep. 11(1), 1–15 (2021)
Souayeh, B.; Ramesh, K.; Hdhiri, N.; Yasin, E.; Alam, M.W.; Alfares, K.; Yasin, A.: Heat transfer attributes of gold–silver–blood hybrid nanomaterial flow in an EMHD peristaltic channel with activation energy. Nanomaterials 12(10), 1615 (2022)
Yacob, N.A.; Ishak, A.; Pop, I.: Falkner-Skan problem for a static or moving wedge in nanofluids. Int. J. Therm. Sci. 50(2), 133–139 (2011)
Kebede, T.; Haile, E.; Awgichew, G.; Walelign, T.: Heat and mass transfer analysis in unsteady flow of tangent hyperbolic nanofluid over a moving wedge with buoyancy and dissipation effects. Heliyon 6(4), e03776 (2020)
Gopi Krishna, S.; Shanmugapriya, M.; Sundareswaran, R.; Kumar, P.S.: MANFIS approach for predicting heat and mass transport of bio-magnetic ternary hybrid nanofluid using Cu/Al2O3/ MWCNT nanoadditives. Biomass Convers. Biorefinery (2022). https://doi.org/10.1007/s13399-022-02989-x
Ullah, I.; Khan, I.; Shafie, S.: Heat and mass transfer in unsteady MHD slip flow of Casson fluid over a moving wedge embedded in a porous medium in the presence of chemical reaction. Numer. Methods Part. Diff. Equa. 34(5), 1–25 (2018)
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Krishna, S.G., Shanmugapriya, M., Kumar, B.R. et al. Thermal and Energy Transport Prediction in Non-Newtonian Biomagnetic Hybrid Nanofluids using Gaussian Process Regression. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-024-08834-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13369-024-08834-9